Understanding the mechanisms that allow biological species to co-occur is of great interest to ecologists. Here we investigate the factors that influence co-occurrence of members of the genus Protea in the Cape Floristic Region of southwestern Africa, a global hot spot of biodiversity. Due to the binomial nature of our response, a critical issue is to choose appropriate link functions for the regression model. In this paper we propose a new family of flexible link functions for modeling binomial response data. By introducing a power parameter into the cumulative distribution function (c.d.f.) corresponding to a symmetric link function and its mirror reflection, greater flexibility in skewness can be achieved in both positive and negative directions. Through simulated data sets and analysis of the Protea co-occurrence data, we show that the proposed link function is quite flexible and performs better against link misspecification than standard link functions.
"A new class of flexible link functions with application to species co-occurrence in cape floristic region." Ann. Appl. Stat. 7 (4) 2180 - 2204, December 2013. https://doi.org/10.1214/13-AOAS663